How can I physically generate a square with two 4x4 squares, three 3x3 squares, four 2x2 squares and 4 1x1 squares?

Question

"George has two 4x4 squares, three 3x3 squares, four 2x2 squares, and four 1x1 squares. Draw a diagram to show how she could place some or all of these squares together without gaps or overlaps to make a square that is a big as possible." (From Math Quest 11)

Please provide a visual diagram.

Sadie Allen · Accepted Answer

The maximum possible size is #7xx7#...

Though the given squares are large enough to cover a total area of #79# units, it is not possible to arrange a subset of them into an #8xx8# square.

The largest possible square is #7xx7#...

Avery Allen · Answer

Make a square with an area of #64# square units.

If you work out the total area of all the squares, we have: #2xx4xx4 = 32# #3xx3xx3 = 27# #4xx2xx2 = 16# #4xx1xx1 = ul4# TOTAL = #79# square units The biggest square that can be made is one with an area of #64#, square units, which means that each of the sides must be #8# units long. Note the use of the phrase, "....how she could place all or some of them"... meaning you can have some squares left over. #79-64 = 15# square units units not used. At this stage there is a bit of trial and error in fitting all the squares together. Start by placing the two biggest squares (#4xx4#), then the smaller ones, until they all fit. I am not able to give a drawing, but with these hints to get you started, I am sure you will manage.

How can I physically generate a square with two 4x4 squares, three 3x3 squares, four 2x2 squares and 4 1x1 squares?

"George has two 4x4 squares, three 3x3 squares, four 2x2 squares, and four 1x1 squares. Draw a diagram to show how she could place some or all of these squares together without gaps or overlaps to make a square that is a big as possible." (From Math Quest 11) Please provide a visual diagram.

"George has two 4x4 squares, three 3x3 squares, four 2x2 squares, and four 1x1 squares. Draw a diagram to show how she could place some or all of these squares together without gaps or overlaps to make a square that is a big as possible." (From Math Quest 11)

Please provide a visual diagram.